Operational Earthquake Forecasting Research Articles

SuiETAS: Developing and Testing ETAS-Based Earthquake Forecasting Models for Switzerland

ABSTRACT We present the development and testing of multiple epidemic-type aftershock sequence (ETAS)-based earthquake forecasting models for Switzerland, aiming to identify suitable candidate models for operational earthquake forecasting (OEF) at the Swiss Seismological Service. We consider seven model variants: four variants use parameters obtained through fitting the ETAS model to the Swiss earthquake catalog, and three use generic parameters that were fit to Californian seismicity or global seismicity from regions tectonically similar to Switzerland. The model variants use different pieces of information from the current state-of-the-art time-independent earthquake rate forecast underlying the Swiss seismic hazard model (SUIhaz2015), and one is calibrated on a larger local data set that includes smaller earthquakes by allowing a time-dependent estimate of the completeness magnitude. We test all variants using pseudoprospective short-term (7-day) forecasting experiments and retrospective long-term (30-year) consistency tests. Our results suggest that all ETAS-based models outperform the time-independent SUIhaz2015 forecast in the short term, but two of the model variants overestimate event numbers in the long term. ETAS parameters are found not to be universally transferrable across tectonic regimes, and region-specific calibration is found to add value over generic parameters. Finally, we rank all model variants based on six criteria, including the results of the pseudoprospective and retrospective tests, as well as other criteria such as model run time or consistency with the existing long-term model, using a multicriteria decision analysis approach. Based on this ranking, we propose the ETAS model calibrated on the Swiss catalog, and with the spatial background seismicity distribution of SUIhaz2015 as the ideal candidate for the first Swiss OEF system. All procedures and choices involved in the development and testing of the Swiss ETAS model follow recently established expert recommendations and can act as a reference in the establishment of time-variant earthquake forecasting models for other regions.

Towards a dynamic earthquake risk framework for Switzerland

Abstract. Scientists from different disciplines at ETH Zurich are developing a dynamic, harmonised, and user-centred earthquake risk framework for Switzerland, relying on a continuously evolving earthquake catalogue generated by the Swiss Seismological Service (SED) using the national seismic networks. This framework uses all available information to assess seismic risk at various stages and facilitates widespread dissemination and communication of the resulting information. Earthquake risk products and services include operational earthquake (loss) forecasting (OE(L)F), earthquake early warning (EEW), ShakeMaps, rapid impact assessment (RIA), structural health monitoring (SHM), and recovery and rebuilding efforts (RRE). Standardisation of products and workflows across various applications is essential for achieving broad adoption, universal recognition, and maximum synergies. In the Swiss dynamic earthquake risk framework, the harmonisation of products into seamless solutions that access the same databases, workflows, and software is a crucial component. A user-centred approach utilising quantitative and qualitative social science tools like online surveys and focus groups is a significant innovation featured in all products and services. Here we report on the key considerations and developments of the framework and its components. This paper may serve as a reference guide for other countries wishing to establish similar services for seismic risk reduction.

What Is the Effect of Seismic Swarms on Short-Term Seismic Hazard and Gutenberg-Richter b-Value Temporal Variation? Examples from Central Italy, October–November 2023

A seismic hazard can be quantified by using probabilities. Modern seismic forecasting models (e.g., Operational Earthquake Forecasting systems) allow us to quantify the short-term variations in such probabilities. Indeed these probabilities change with time and space, in particular after strong seismic events. However, the short-term seismic hazard could also change during seismic swarms, i.e., a sequence with several small-/medium-sized events. The goal of this work is to quantify these changes, using the Italian Operational Earthquake Forecasting system, and also estimate the variations in the Gutenberg–Richter b-value. We focus our attention on three seismic swarms that occurred in Central Italy in October–November 2023. Our results indicate that short-term variations in seismic hazard are limited, less than an order of magnitude, and also that b-value variations are not significant. Placing our findings in a more general context, we can state that according to currently available models and catalogs, the occurrence of seismic swarms does not significantly affect the short-term seismic hazard.

Operational Earthquake Forecasting in Japan: A Study of Municipal Government Planning for an Earthquake Advisory or Warning in the Nankai Region

Abstract A team of social scientists from the United States and Japan has conducted a study exploring the extent to which municipal governments in Japan have developed plans for response to an operational earthquake forecast from the Japan Meteorological Agency (JMA), indicating that seismic activity in the Nankai trough region has elevated the short-term probability that a major earthquake may occur. Employing both survey research and in-depth interviews, the team explored various aspects of the history and science behind the alerting system, guidance from the national government of Japan, and planning by local jurisdictions for a possible future Nankai trough major earthquake. The survey included questions regarding planning actions included in response plans for receipt of “special earthquake warning information” as well as questions regarding challenges in the planning process, expectations that an earthquake would follow the issuance of an alert, and whether planning would reduce the number of fatalities and injuries. We also conducted in-depth interviews that explored the scientific basis for the alerting system and asked working disaster managers in the Nankai region what they had done to plan and the reasons for not planning if plans had not been developed. We received 469 responses from a total of 736 jurisdictions that comprise the Nankai region—a response rate of 63.7%. We conducted a total of 17 in-depth interviews. In general, we found that a majority of jurisdictions have response plans for receipt of an alert from the JMA; however, the plans lacked a number of planning elements considered important from a disaster management perspective. In addition, many smaller jurisdictions lacked the staffing, resources, and guidance to form comprehensive response plans. Our report identifies both the strengths and weaknesses of existing plans, and outlines a program for improving planning in the region.

Social Science Contributions to Earthquake Warnings: Commemorating the Work of Dennis S. Mileti

The pioneering work of Dennis Mileti and those with whom he collaborated have established a sound basis in understanding how human beings behave when encountering hazard warnings. His work greatly expanded our understanding of the social environment into which warnings are issued and provided clear guidelines on how warnings should be delivered to optimize behavioral compliance; how warning message content can be construed to motivate protective actions; and why people may fail to comply or delay actions after receipt of a warning. This paper addresses Mileti’s work in earthquake warnings, first in the context of earthquake predictions and later, as optimism waned that accurate earthquake predictions were possible, as his insights were applied to newer approaches in the form of earthquake early warnings and operational earthquake forecasting. This paper will first briefly trace the historical development of approaches to warn of a potentially damaging earthquake because it is important to place Mileti’s work in the historical context in which it was carried out. It then assesses the manner in which the current methods of earthquake warning for short- and intermediate-term time frames via earthquake early warning and operational earthquake forecasting have benefited from Mileti’s very significant observations and insights. His work in evaluating and clarifying the social environment in which warnings are issued is an important and enduring element of his legacy, has significantly influenced how hazard warnings are now formulated, and has greatly shaped the work of those of us who carry on the study of hazard warning systems.

Operational Earthquake Forecasting in Italy: validation after 10 yr of operativity

SUMMARYIn this paper, we gather and take stock of the results produced by the Operational Earthquake Forecasting (OEF) system in Italy, during its first 10 yr of operativity. The system is run in real-time: every midnight and after each ML 3.5+ event, it produces the weekly forecast of earthquakes expected by an ensemble model in each cell of a spatial grid covering the entire Italian territory. To evaluate the performance skill of the OEF-Italy forecasts, we consider here standard tests of the Collaboratory for the Study of Earthquake Predictability, which have been opportunely adapted to the case of the overlapped weekly OEF forecasts; then we also adopt new performance measures borrowed from other research fields, like meteorology, specific to validate alarm-based systems by a binary criterion (forecast: yes/no; occurrence: yes/no). Our final aim is to: (i) investigate possible weaknesses and room for improvements in the OEF-Italy stochastic modelling, (ii) provide performance measures that could be helpful for stakeholders who act through a boolean logic (making an action or not) and (iii) highlight possible features in the Italian tectonic seismic activity.

Bayesian modeling of the temporal evolution of seismicity using the ETAS.inlabru package

The epidemic type aftershock sequence (ETAS) model is widely used to model seismic sequences and underpins operational earthquake forecasting (OEF). However, it remains challenging to assess the reliability of inverted ETAS parameters for numerous reasons. For example, the most common algorithms just return point estimates with little quantification of uncertainty. At the same time, Bayesian Markov chain Monte Carlo implementations remain slow to run and do not scale well, and few have been extended to include spatial structure. This makes it difficult to explore the effects of stochastic uncertainty. Here, we present a new approach to ETAS modeling using an alternative Bayesian method, the integrated nested Laplace approximation (INLA). We have implemented this model in a new R-Package called ETAS.inlabru, which is built on the R packages R-INLA and inlabru. Our study has included extending these packages, which provided tools for modeling log-Gaussian Cox processes, to include the self-exciting Hawkes process that ETAS is a special case of. While we just present the temporal component here, the model scales to a spatio-temporal model and may include a variety of spatial covariates. This is a fast method that returns joint posteriors on the ETAS background and triggering parameters. Using a series of synthetic case studies, we explore the robustness of ETAS inversions using this method of inversion. We also included runnable notebooks to reproduce the figures in this article as part of the package's GitHub repository. We demonstrate that reliable estimates of the model parameters require that the catalog data contain periods of relative quiescence, as well as triggered sequences. We explore the robustness of the method under stochastic uncertainty in the training data and show that the method is robust to a wide range of starting conditions. We show how the inclusion of historic earthquakes prior to the modeled time window affects the quality of the inversion. Finally, we show that rate-dependent incompleteness of earthquake catalogs after large earthquakes have a significant and detrimental effect on the ETAS posteriors. We believe that the speed of the inlabru inversion, which includes a rigorous estimation of uncertainty, will enable a deeper exploration of how to use ETAS robustly for seismicity modeling and operational earthquake forecasting.

NESTOREv1.0: A MATLAB Package for Strong Forthcoming Earthquake Forecasting

AbstractThis article presents the first publicly available version of the NExt STrOng Related Earthquake (NESTORE) software (NESTOREv1.0) designed for the statistical analysis of earthquake clusters. NESTOREv1.0 is a MATLAB (www.mathworks.com/products/matlab, last accessed August 2022) package capable of forecasting strong aftershocks starting from the first hours after the mainshocks. It is based on the NESTORE algorithm, which has already been successfully applied retrospectively to Italian and California seismicity. The code evaluates a set of features and uses a supervised machine learning approach to provide probability estimates for a subsequent large earthquake during a seismic sequence. By analyzing an earthquake catalog, the software identifies clusters and trains the algorithm on them. It then uses the training results to obtain forecasting for a test set of independent data to estimate training performance. After appropriate testing, the software can be used as an Operational Earthquake Forecasting (OEF) method for the next stronger earthquake. For ongoing clusters, it provides near-real-time forecasting of a strong aftershock through a traffic light classification aimed at assessing the level of concern. This article provides information about the NESTOREv1.0 algorithm and a guide to the software, detailing its structure and main functions and showing the application to recent seismic sequences in California. By making the NESTOREv1.0 software available, we hope to extend the impact of the NESTORE algorithm and further advance research on forecasting the strongest earthquakes during seismicity clusters.

On the calculation of smoothing kernels for seismic parameter spatial mapping: methodology and examples

Abstract. Spatial mapping is one of the most useful methods to display information about the seismic parameters of a certain area. As in b-value time series, there is a certain arbitrariness regarding the function selected as smoothing kernel (which plays the same role as the window size in time series). We propose a new method for the calculation of the smoothing kernel as well as its parameters. Instead of using the spatial cell-event distance we study the distance between events (event-event distance) in order to calculate the smoothing function, as this distance distribution gives information about the event distribution and the seismic sources. We examine three different scenarios: two shallow seismicity settings and one deep seismicity catalog. The first one, Italy, allows calibration and showcasing of the method. The other two catalogs: the Lorca region (Spain) and Vrancea County (Romania) are examples of different function fits and data treatment. For these two scenarios, the prior to earthquake and after earthquake b-value maps depict tectonic stress changes related to the seismic settings (stress relief in Lorca and stress build-up zone shifting in Vrancea). This technique could enable operational earthquake forecasting (OEF) and tectonic source profiling given enough data in the time span considered.

Calibration of a Bayesian spatio-temporal ETAS model to the June 2000 South Iceland seismic sequence

SUMMARY The reliable forecasting of seismic sequences following a main shock has practical implications because effective post-event response is crucial in earthquake-stricken regions, aftershocks can progressively cause increased damage and compound economic losses. In the South Iceland Seismic Zone (SISZ), one of two large transform zones in Iceland where earthquake hazard is the highest, an intense seismic sequence took place during 17–24 June 2000, starting with a ${M}_{\rm{w}}$ 6.4 main shock on 17 June 2000, followed by another ${M}_{\rm{w}}$ 6.5 main shock four days later and on a different fault. Both earthquakes caused considerable damage and incurred heavy economic losses. They were immediately followed by intense aftershock activity on the causative faults and triggered earthquakes as far as 80 km away along the transform zone. To investigate the feasibility of forecasting the progression of such complex sequences, we calibrated a spatio-temporal epidemic-type aftershock sequence (ETAS) clustering model to the June 2000 seismic sequence in the framework of Bayesian statistics. Short-term seismicity forecasts were carried out for various forecasting intervals and compared with the observations, the first generated a few hours after the first main shock and followed by daily forecasts. The reliability of the early forecasts was seen to depend on the initial model parameters. By using an adaptive parameter inference approach where the posteriors from each preceding forecasting interval served as informative priors for the next, the fast convergence of the parametric values was ensured. As a result, the 16–84 percentile range of the forecasted number of events captured the actual number of observed events in all daily forecasts, and the model exhibited a strong spatial forecasting ability, even only a few hours after the main shock, and over all subsequent daily forecasts. We present the spatio-temporal ETAS parameters for the June 2000 sequence as ideal candidates of prior estimates for future operational earthquake forecasting of other Icelandic aftershock sequences. Past seismic sequences need to be analysed retrospectively to confirm the stability of the parameters of this study, effectively enable the application of the Bayesian ETAS model as an operational earthquake forecasting system for aftershocks in Iceland.

Short-term Bayesian ETAS spatiotemporal forecasting of the Ölfus 2008 earthquake sequence in Iceland

Strong earthquakes occurring frequently in south Iceland are always characterized by intense aftershock activity. The aftershock sequences cause progressive damages to structures and considerable psychological strain on inhabitants as the threat of upcoming large earthquakes looms. In this study, we apply a Bayesian epidemiological spatiotemporal aftershock sequence (ETAS) clustering model to forecast the aftershock sequence that commenced with the damaging 29 May 2008 Mw6.3 Ölfus earthquake. The forecast is carried out manually but in a framework of a provisional operational earthquake forecasting (OEF) system and based on an informative set of ETAS parameters derived from the strong June 2000 sequence in the region. We show that the short-term forecasts are unreliable at the early stages of the ongoing seismic sequence due to incomplete aftershocks collected to feed the Bayesian updating procedure of the ETAS model parameters, mainly during the first hours after the Ölfus mainshock. In contrast, issuing 24-h long forecasts, starting 6–8 h after the mainshock gives the best forecasting results. We allow the daily forecasts to adapt to the ongoing 2008 sequence using the adaptive prior estimation method, i.e., by assigning an informative prior distribution to ETAS parameters for the subsequent forecasting interval based on the preceding ETAS parameter posterior distributions. The parametric posteriors do not show narrow distributions, thus indicating inconsistent forecasting performance, both in stark contrast to the June 2000 sequence. Regardless, our results provide a quantitative estimate of the reliability of the forecasts which is a prerequisite for evaluating their usefulness to civil protection.

PyCSEP: A Python Toolkit for Earthquake Forecast Developers

Abstract The Collaboratory for the Study of Earthquake Predictability (CSEP) is an open and global community whose mission is to accelerate earthquake predictability research through rigorous testing of probabilistic earthquake forecast models and prediction algorithms. pyCSEP supports this mission by providing open-source implementations of useful tools for evaluating earthquake forecasts. pyCSEP is a Python package that contains the following modules: (1) earthquake catalog access and processing, (2) representations of probabilistic earthquake forecasts, (3) statistical tests for evaluating earthquake forecasts, and (4) visualization routines and various other utilities. Most significantly, pyCSEP contains several statistical tests needed to evaluate earthquake forecasts, which can be forecasts expressed as expected earthquake rates in space–magnitude bins or specified as large sets of simulated catalogs (which includes candidate models for governmental operational earthquake forecasting). To showcase how pyCSEP can be used to evaluate earthquake forecasts, we have provided a reproducibility package that contains all the components required to re-create the figures published in this article. We recommend that interested readers work through the reproducibility package alongside this article. By providing useful tools to earthquake forecast modelers and facilitating an open-source software community, we hope to broaden the impact of the CSEP and further promote earthquake forecasting research.

Analysis of Radon Measurements in Relation to Daily Seismic Activity Rates in the Vrancea Region, Romania.

Many previous research studies have shown how local and even regional earthquakes can significantly affect the release of radon in the soil. The aim of this work is to investigate the relationship between radon measurements and the daily seismic activity rate and develop a methodology that allows estimating the seismic activity rate using only radon measurements. To carry out this study, the earthquake catalogue of the Vrancea region (Romania) has been used to estimate the daily seismic activity rate during a given time period, in which radon measurements were also recorded, from January 2016 to September 2020. The Vrancea zone represents the most active seismic zone in Europe and is located on the eastern edge of the strongly bent Carpathian arc. In the case of the radon measurements, seasonal behaviours and linear trends due to non-seismic factors have been identified and subsequently removed. The discrete wavelet transform has been used to analyse the radon signal at two different scales: long and short periods. From the analysis carried out on a long-period scale, an approximate linear relationship has been obtained between the radon series and the daily seismic activity rate, which provides insights into the behaviour of the seismic activity in the study region with only the radon information. In addition, the study reveals certain characteristics that could be used as precursors of earthquakes at different scales: weeks in the case of the estimated daily seismic activity rate, and days in the case of the short-period signal obtained by the wavelet analysis. The results obtained for this region allow us to hope that the analysis of the radon time series can become an effective complement to the conventional seismic analysis used in operational earthquake forecasting.

Variations in hazard during earthquake sequences between 1995 and 2018 in western Greece as evaluated by a Bayesian ETAS model

SUMMARY Forecasting the spatio-temporal occurrence of events is at the core of Operational Earthquake Forecasting, which is of great interest for risk management, particularly during ongoing seismic sequences. Epidemic type aftershock sequence (ETAS) models are powerful tools to estimate the occurrence of events during earthquake sequences. In this context, a robust seismicity forecasting framework based on Bayesian-inference has been adapted to the Patras and Aegio region in western Greece (one of the most seismically active parts of Mediterranean), and an incremental adaptive algorithm is introduced to train the priors for ETAS model parameters. The seismicity forecasting is capable of accounting for uncertainty in the model parameters as well as variations in the sequence of events that may happen during the forecasting interval. Six seismic sequences between 1995 and 2018 were selected with main shock moment magnitudes Mw ≥ 6.0. The ETAS model was adapted for each seismic sequence. The number of forecasted events with Mw ≥ 4.5 and their spatial distribution was retrospectively compared with the as-recorded earthquake catalogue, confirming a good agreement between the forecasts and observations. The results show that the adapted model can be used immediately after a severe main shock to statistically predict potentially damaging earthquakes during the ongoing seismic sequence. The seismicity forecasts were translated to short-term daily exceedance rates for different thresholds of peak ground acceleration. The results reveal that the seismic hazard increased by up to 33 times in the case of the damaging 1995 Mw 6.5 earthquake in the city of Aegio. However, the results confirmed that in all six studied sequences, the increased seismic hazard decayed rapidly during the 2 d after the main shock, and remained relatively high in the following days (roughly ten times the long-term time-independent hazard).

Identification and Temporal Characteristics of Earthquake Clusters in Selected Areas in Greece

The efficiency of earthquake clustering investigation is improved as we gain access to larger datasets due to the increase of earthquake detectability. We aim to demonstrate the robustness of a new clustering method, MAP-DBSCAN, and to present a comprehensive analysis of the clustering properties in three major seismic zones of Greece during 2012–2019. A time-dependent stochastic point model, the Markovian Arrival Process (MAP), is implemented for the detection of change-points in the seismicity rate and subsequently, a density-based clustering algorithm, DBSCAN, is used for grouping the events into spatiotemporal clusters. The two-step clustering procedure, MAP-DBSCAN, is compared with other existing methods (Gardner-Knopoff, Reasenberg, Nearest-Neighbor) on a simulated earthquake catalog and is proven highly competitive as in most cases outperforms the tested algorithms. Next, the earthquake clusters in the three areas are detected and the regional variability of their productivity rates is investigated based on the generic estimates of the Epidemic Type Aftershock Sequence (ETAS) model. The seismicity in the seismic zone of Corinth Gulf is characterized by low aftershock productivity and high background rates, indicating the dominance of swarm activity, whereas in Central Ionian Islands seismic zone where main shock-aftershock sequences dominate, the aftershock productivity rates are higher. The productivity in the seismic zone of North Aegean Sea vary significantly among clusters probably due to the co-existence of swarm activity and aftershock sequences. We believe that incorporating regional variations of the productivity into forecasting models, such as the ETAS model, it might improve operational earthquake forecasting.

Validation of the Epidemic-Type Aftershock Sequence (ETAS) Models for Simulation-Based Seismic Hazard Assessments

AbstractModerate-to-large-magnitude earthquakes induce considerable short-to-medium-term increases in seismic hazard, due to the subsequent occurrence of aftershocks. Most studies on aftershock occurrence models focus on their performance as part of Operational Earthquake Forecasting (i.e., the real- or near-real-time predictions of ongoing sequences). Aftershock model validation on a longer timescale is scarcely dealt with in the literature, however. This study addresses this research gap by validating the medium-term (i.e., months to years) performance of an advanced formulation of the epidemic-type aftershock sequence (ETAS) model for potential future implementation in simulation-based probabilistic seismic hazard analyses (PSHAs). The aim is to determine whether the considered ETAS model can forecast adequate numbers of aftershocks, and consistent spatial and magnitude–frequency distributions, for three years after a given moderate-to-large-magnitude mainshock. Two different calibration procedures (region wide and sequence averaged) are used to investigate the ability of resulting ETAS models to describe common characteristics of the considered sequences. The region-wide methodology is based on the entire catalog of a large geographic area and is the conventional approach for calibrating ETAS models. The second calibration methodology is instead based on sequence-specific data. The validation procedure employs only out-of-sample (i.e., retrospective) testing, and its evaluation metrics are the catalog-based scores recently proposed for the Collaboratory for the Study of Earthquake Predictability framework. It is demonstrated using the New Zealand catalog (1990–2020), including seven sequences in the period 1990–2020, in two case studies. Resulting test scores indicate that the conventional region-wide calibration approach is not suitable for building an ETAS model to use in simulation-based PSHA. Sequence-averaged ETAS models are generally more acceptable, in terms of both numbers of aftershocks and consistent spatial and magnitude–frequency distributions. The findings of this study can be used to guide future implementations of the considered ETAS formulation, possibly in combination with a simulation-based mainshock PSHA.

An Operational Earthquake Forecasting Experiment for Israel: Preliminary Results

Operational Earthquake Forecasting (OEF) aims to deliver timely and reliable forecasts that may help to mitigate seismic risk during earthquake sequences. In this paper, we build the first OEF system for the State of Israel, and we evaluate its reliability. This first version of the OEF system is composed of one forecasting model, which is based on a stochastic clustering Epidemic Type Earthquake Sequence (ETES) model. For every day of the forecasting time period, January 1, 2016 - November 15, 2020, the OEF-Israel system produces a weekly forecast for target earthquakes with local magnitudes greater than 4.0 and 5.5 in the entire State of Israel. Specifically, it provides space-time-dependent seismic maps of the weekly probabilities, obtained by using a fixed set of the model’s parameters, which are estimated through the maximum likelihood technique based on a learning period of about 32 years (1983–2015). According to the guidance proposed by the Collaboratory for the Study of Earthquake Predictability (CSEP), we also perform the N- and S-statistical tests to verify the reliability of the forecasts. Results show that the OEF system forecasts a number of events comparable to the observed one, and also captures quite well the spatial distribution of the real catalog with the exception of two target events that occurred in low seismicity regions.

Missing Earthquake Data Reconstruction in the Space‐Time‐Magnitude Domain

AbstractShort term aftershock incompleteness (STAI) can strongly bias any analysis built on the assumption that seismic catalogs have a complete record of events. Despite several attempts to tackle this issue, we are far from trusting any data set in the immediate future of a large shock occurrence. Here, we introduce RESTORE (REal catalogs STOchastic REplenishment), a Python toolbox implementing a stochastic gap‐filling method, which automatically detects the STAI gaps and reconstructs the missing events in the space‐time‐magnitude domain. The algorithm is based on empirical earthquake properties and relies on a minimal number of assumptions about the data. Through a numerical test, we show that RESTORE returns an accurate estimation of the number of missed events and correctly reconstructs their magnitude, location, and occurrence time. We also conduct a real‐case test, by applying the algorithm to the 6.2 Amatrice aftershocks sequence. The STAI‐induced gaps are filled and missed earthquakes are restored in a way which is consistent with data. RESTORE, which is made freely available, is a powerful tool to tackle the STAI issue, and will hopefully help to implement more robust analyses for advancing operational earthquake forecasting and seismic hazard assessment.

Comparing Short-Term Seismic and COVID-19 Fatality Risks in Italy

Abstract Risks assessment and risks comparison are basic concepts for emergency management. In the fields of earthquake engineering and engineering seismology, the operational earthquake loss forecasting (OELF) is the research frontier for the assessment of short-term seismic risk. It combines seismicity models, continuously updated based on ground-motion monitoring (i.e., operational earthquake forecasting), with large-scale vulnerability models for the built environment and exposure data. With the aim of contributing to the discussion about capabilities and limitations of OELF, the study presented aims at comparing the OELF results and the fatality risk (based on fatality data) related to coronavirus 2019 (COVID-19) that, at the time of writing, is perceived as very relevant and required unprecedented risk reduction measures in several countries, most notably Italy. Results show that, at a national scale in Italy, the COVID-19 risk has been higher than the seismic risk during the two pandemic waves even if, at the end of the so-called lockdown, the evolution of the pandemic suggested the possibility (not realized) of reaching a situation of comparable seismic and COVID-19 risks in a few weeks. Because the two risks vary at a local scale, risks comparison was also carried out on a regional basis, showing that, before the beginning of the second wave, in some cases, the seismic risk, as assessed by means of OELF, was larger than the pandemic one.

An Energy-Dependent Earthquake Moment–Frequency Distribution

ABSTRACTThe magnitude–frequency distribution (MFD) of many earthquake catalogs is well described by the Gutenberg–Richter (GR) law or its tapered version (TGR). This distribution is usually extrapolated to any subsets of the space–time window covered by the catalog. However, some empirical observations and logical thoughts may raise doubts about the validity of this extrapolation. For example, according to the elastic rebound theory, we may assert that the probability of a strong shock nucleating within a short-time interval in a small area A just ruptured by another strong event should be lower than that expected by GR (or TGR): a lot of energy has already been released, and it takes time to recover to the previous state. Here, we put forward a space–time modification of the TGR, named energy-dependent TGR (TGRE) in which the corner seismic moment becomes a time-varying energy function depending on (1) the conceivable strongest shock that may nucleate in A; (2) the time elapsed since the last strong earthquake that reset the elastic energy in A to a residual value; and (3) the rate of the energy recovery, linked to the recurrence time of the fault(s) involved. The model also verifies an invariance condition: for large space–time windows, the occurrence of a strong shock does not affect significantly the whole elastic energy available, that is, the TGRE becomes the TGR. The model is simple and rooted in clearly stated assumptions. To evaluate its reliability and applicability, we apply it to the 1992 Landers sequence. As expected by TGRE, we find that the MFD close to the fault system interested by the mainshock (Mw 7.3) differs from that of earthquakes off-fault, showing a lower corner magnitude. We speculate that TGRE may be profitably used in operational earthquake forecasting and that it explains the empirical observation that the strongest aftershocks nucleate always outside the mainshock fault.